Two ways to compute moments in families of L-functions

About 20 years ago, Conrey, Farmer, Keating, Rubinstein and Snaith came up with a recipe which predicts the asymptotic formulas for moments of families of L-functions. At about the same time, Diaconu, Goldfeld and Hoffstein used multiple Dirichlet series and predicted the same asymptotics in a different way. In this talk, we will present the approaches and show that they are closely related.